1. Anisotropy Safari
Matt Current Jr.1,2,4, Kevin Lee1,2,5,
Dr. Santasri Basu1,3, Dr. Jack E. McCrae1,3
1Department of Engineering Physics, 2Southwestern Ohio Council
for Higher Education (SOCHE), 3Oak Ridge Institute for Science
and Education (ORISE), 4Augsburg College, 5University of Virginia

2. “I am an old man now, and when I die and go
to heaven there are two matters on which I
hope for enlightenment. One is quantum
electrodynamics, and the other is the turbulent
motion of fluids. And about the former I am
rather optimistic.”
- Horace Lamb, in an address to the British
Association for the Advancement of Science,
1932 [2]
Hydrodynamics (1895) and Dynamical
Theory of Sound (1910)
Introduction to Turbulence
[1][3]
“[Turbulence is] the most important unsolved
problem of classical physics.” - Richard
Feynman [4]
Nobel Prize in Physics (1965) , Rogers Commission
(1980s)

3. Overview
• What exactly is being investigated on this safari?
• Method and Apparatus used
• Anisotropy Metric 1: Slope Variance Ratios
• Anisotropy Metric 2: Differential Tilt Variance Ratios
• Conclusion
• Looking Forward

4. What to Investigate
• Is turbulence always isotropic? Kolmogorov Theory makes the assumption of isotropic
turbulence. However, turbulence might prefer the horizontal (x) or vertical (y) directions
during times of the day when turbulence is weak.
Un-even Cold Ground Un-even Warm Ground
After Sunrise
(6 AM – 8 AM EST*)
After Sunset
(9 PM – 10 PM EST*)
Sun begins to
heat up ground Warm air
wants to
rise.
Warm air
rises in
plumes due to
uneven
ground. Once
a plume
begins to rise,
all the warm
air around
follows it up.
Cold air from
night cools down
the ground
Air is not a good radiator, so
cold air from night gets
trapped underneath the hot
air leftover from the daytime
Air is organized in stratified layers
often called “pancake – shaped”.
*Time depends on the location of the path and time of year.

5. Apparatus
HeNe Laser
Setup – 2.2 mW
Distance: ~200 m
Hartmann Turbulence
Sensor (Trailer-mounted)
Turbulence
Wavefront Without
Turbulence
Wavefront With
Turbulence
We can measure the tilts on the
wavefront using the HTS. This
method allows us to see if
turbulence is more prominent in
the x or y directions.
[5]
Grassy Field

6. Measuring the Wavefront
[6]
• Central Obscuration due to
telescope design
• 700 active subapertures
[7]
• As turbulence
increases the dots
move more around in
their respective
boxes.
• The dots slow down
as turbulence
decreases.

7. Variance Ratio – Kirtland, NM
[8]
• A similar experiment has been conducted
in Kirtland, NM.
• One metric of isotropy vs. anisotropy used
was taking the variance of the distance
from the center of each box to its
respective dot in both the x and y
directions and the plotting the ratio.
• Isotropic turbulence should have a ratio of
one, while anisotropic turbulence should
have a ratio greater or less than one.
• There was some evidence to suggest that
there had been anisotropic turbulence,
but for the most part, the turbulence was
found to be isotropic. However, the data
did not span a very long time period.

8. Variance Ratio – Wright Patterson, OH
(Zoomed In)
• In order to obtain a more complete story, data was collected over a longer period of time, namely over almost all the 24 hours
in a given day.
• It can now be seen that during the day (1200 – 2400 UTC), the turbulence is very isotropic with a tight distribution around 1.
• During sunrise (0600-1200 UTC), the turbulence is still fairly isotropic, but the distribution is a lot more spread out than during
the day.
• Around sunset (0000-0200 UTC), the turbulence appears to be anisotropic with a preference in the horizontal direction.
• At night (0200-0600 UTC), it is unclear what is going on.

9. Variance Ratio – Wright Patterson, OH
(Zoomed In)
• The data was not collected all at one time, but was actually collected over a period of a couple weeks.
• It can be seen that the sunrise, day, and sunset trends occur pretty consistently from day to day.

10. Mask X-pairs and Y-pairs

11. Differential Tilts – Kirtland, NM
[8]
• Another metric that was used in Kirtland was plotting the ratio of the differential tilt variances in both the x and y directions.
• According to the Kolmogorov Theory of isotropic turbulence, the ratios should be the same and should follow the black curve
plotted in the above graph.
• Using this metric, they found that during certain times of the day, when the turbulence was at its weakest, the data showed
some evidence for anisotropy.

12. Differential Tilts – Wright Patterson, OH
Time: Sunrise (0600-1200 UTC)
• During the sunrise time, the turbulence seems to be fairly isotropic.
• The X/Y ratios on the left stay statistically close to the isotropic value of one.
• The Longitudinal/Transverse ratios are close together and follow the expected curve.

13. • During the day, the data implies that the turbulence is very isotropic.
• The Longitudinal/Transverse ratios are practically identical.
• The X/Y ratios are almost all within 0.1 of one.
• The unusual aspect of the data that comes out is that the Longitudinal/Transverse ratios do not follow the
theoretical curve. It is unclear why this occurs.
Differential Tilts – Wright Patterson, OH
Time: Day (1200-2400 UTC)

14. • At sunset, a nice separation between the curves can be seen, implying some anisotropy with a preferred
horizontal direction.
• The X/Y ratios are more than a standard deviation from one.
Differential Tilts – Wright Patterson, OH
Time: Sunset (0000-0200 UTC)

15. • Finally, it is unclear what is going on during the night…still.
• While there is something unusual going on, the error bars are too big for any statistical significance.
Differential Tilts – Wright Patterson, OH
Time: Night (0200-0600 UTC)

16. Conclusion
• For most of the day, measured turbulence appears
to be consistent with the Kolmogorov Theory,
meaning that it is isotropic and does not prefer a
direction.
• However, during sunset the turbulence no longer
appears to follow the Kolmogorov Theory, but rather
seems to form a “pancake-shaped” anisotropic
layered structure.
• More data needs to be collected through the night to
get a better idea of what the turbulence is doing.

17. Looking Forward
• More night time data needs to be collected.
• Look into possible reasons that the differential tilt ratios do not follow
the trend predicted with the Kolmogorov Theory even when the
turbulence appears isotropic.
• This experiment was done over a grassy field. Future experiments
should be conducted over various terrain such as concrete, gravel,
and water. They should also be measured at various distances.
• Various ambient weather measurements can also be used to
calculate turbulence strength and predict the whether turbulence is
isotropic or anisotropic, and interest in comparing that data to the
data collected with this experiment has been shown.

18. References
1. http://www.maths.manchester.ac.uk/about-us/history/horace-lamb/
2. http://turb.seas.ucla.edu/~jkim/sciam/turbulence.html
3. http://www.findagrave.com/cgi-bin/fg.cgi?page=gr&GRid=2562
4. http://usatoday30.usatoday.com/tech/science/columnist/vergano/2006-
09-10-turbulence_x.htm
5. http://www.everystockphoto.com/photo.php?imageId=224090
6. Brennan, T. J., & Mann, D. C. (2010). Estimation of optical turbulence
characteristics from Shack Hartmann wavefront sensor
measurements.Advanced Wavefront Control: Methods, Devices, and
Applications VIII. doi:10.1117/12.862808
7. http://www.thorlabs.com/NewGroupPage9_PF.cfm?ObjectGroup_ID=2
861
8. Sanchez, D. J. (2015). Use of Anisotropy Data to Gauge Komogarity -
Application is Made to the RACHL Experiment. Imaging and Applied
Optics 2015. doi:10.1364/pcdvtap.2015.pt4c.3

19. Questions?